Final answer:
The quadratic equation 3cot² - 5cot = -2 factors to give cot = 2/3 or cot = 1; thus, the correct answer is A. 1, which is included in the options provided.
Step-by-step explanation:
The equation given is a quadratic in terms of cotangent: 3cot2 - 5cot + 2 = 0. To solve this equation for cot, we can factor it as (3cot - 2)(cot - 1) = 0, which gives us two possible solutions for cotangent: cot = 2/3 or cot = 1. The options provided in the question include cot = 1, so the correct answer is A. 1.